3. [Sometimes, it's useful to think about what fraction of a consumer's moneythey spend on each good, rather on how many units they buy.(a) Show that every x EX(p,m) can be written as x = f1(m/p₁,0) + f2(0, m/p2 ) +(1-f1-f2)(0,0) for some numbers f1,f2 20 with f1 + f2 ≤1.(b) Let f1 and f2 be as in part (a). Give an expression, in terms of f1 and f2,for the fraction pix₁/m of the consumer's money that they spend on good 1.(c) Let f1 and f2 be as in part (a). Give an expression, in terms of f1 and f2,for the fraction p2x2/m of the consumer's money that they spend on good 2

3. [Sometimes, it's useful to think about what fraction of a consumer's money they spend on each good, rather on how many units they buy. (a) Show that every x EX(p.m) can be written as x = f1( m/p²,0) + f2(0, m/p2 ) + (1-f1-f2)(0,0) for some numbers f1,f2 20 with f1 + f2 ≤1.

3. [Sometimes, it's useful to think about what fraction of a consumer's money they spend on each good, rather on how many units they buy. (a) Show that every x EX(p.m) can be written as x = f1( m/p²,0) + f2(0, m/p2 ) + (1-f1-f2)(0,0) for some numbers f1,f2 20 with f1 + f2 ≤1.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3. [Sometimes, it's useful to think about what fraction of a consumer's money
they spend on each good, rather on how many units they buy.
(a) Show that every x EX(p,m) can be written as x = f1(m/p₁,0) + f2(0, m/p2 ) +
(1-f1-f2)(0,0) for some numbers f1,f2 20 with f1 + f2 ≤1.
(b) Let f1 and f2 be as in part (a). Give an expression, in terms of f1 and f2,
for the fraction pix₁/m of the consumer's money that they spend on good 1.
(c) Let f1 and f2 be as in part (a). Give an expression, in terms of f1 and f2,
for the fraction p2x2/m of the consumer's money that they spend on good 2

Expert Solution

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In economics, a budget constraint represents the set of all possible combinations of goods and services that a consumer can purchase given their limited income and the prices of the goods and services

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